The mandible is the largest and most robust of the facial bones and the only movable of the craniofacial bones. It forms a unity with the related muscles, joints and teeth, and a highly developed masticatory system under the coordination of nerves; therefore, its biomechanical behavior has an important position in various clinical states. Obtaining the various kinetic and static parameters of the mandible is a fundamental part of human biomechanics research and is the basis for the establishment of human mechanical models. Numerous studies (Hart 1992, Korioth 1997, Voo 1996, etc.) have shown that finite element analysis (FEA) can describe the biomechanical properties of mandibular specimens more accurately (correlation coefficient up to 0.992). Therefore, it is particularly important to study the elastic constants of mandibular bone, because if wrong data are quoted, the results can be “wrong by a hair”. The elastic constants of the mandible The mandible has a similar stress-strain relationship with engineering materials, and follows Hooke’s law in the elastic limit. The elastic constants required for modeling include the modulus of elasticity E, shear modulus G, and Poisson’s ratio ν. The modulus of elasticity is a measure of stiffness. For a composite material such as bone tissue, its elastic constants vary with its degree of symmetry. There are 36 elastic constants for anisotropic materials, 21 independent elastic components for complete anisotropy, and 9 for orthotropic anisotropy, which is considered to be simpler and more feasible to reflect the anisotropy of mandibular materials to a certain extent. The relationship between the three is: G=1/2×E/ (1+ν), therefore, only two of the three elastic constants are independent; when the elastic constants are not affected by the direction, i.e., completely symmetric isotropic materials, there are only two elastic constants: Young’s modulus of elasticity (E) and Poisson’s ratio (ν). The human mandible is an anisotropic material. Many large animals, such as sheep and cattle, have mandibles composed mainly of plexiform cortical bone, and the elastic constants are different from those of cortical bone composed of Harvard’s system; in a way, human bone differs from cattle bone in that the former is isotropic in cross-section and the latter is orthogonal and anisotropic, with very different ontogenetic relationships. it is isotropic with E = 7.5 Gpa and ν = 0.4. (However, dog femoral cortical bone exhibits orthogonal anisotropy.) Kawahara et al. measured an E value of 12.8 ± 3.1 Gpa for the Beagle. 3. Elastic modulus of human mandible 3.1 Elastic modulus of human mandibular cortical bone In the oriented structure of mandibular cortical bone, the fiber orientation determines the direction of the combined force and constitutes the force pillar. Many scholars believe that the anisotropic character of the E value of mandibular bone is caused by the orientation of collagen fibers.Lettry et al. studied five (53-106 years old) fresh human mandibles and observed the E values of cortical bone at different sites when taken in the same direction and the E values of cortical bone at the same (adjacent) site when taken in different directions. The E value of cortical bone near the alveolar bone in the premolar region was significantly lower than that of cortical bone away from the alveolar bone (near the inferior margin); the E value of cortical bone near the inferior margin in the molar region was higher than that of cortical bone away from the inferior margin (near the alveolar bone), but there was no statistical difference; the E value of cortical bone in the molar region near the alveolar bone was significantly higher compared with that in the premolar region. The results also showed that the E values of cortical bone tested after cutting at a certain angle to the long axis of the mandibular body (0, 45, and 90 degrees from the long axis, respectively) were different, and the E values decreased with increasing angle. It can be seen that the elastic modulus of mandibular cortical bone has a significant anisotropy. In the study, Lettry also compared the results of Tamatsu et al. using the method described by Bland and found that the storage conditions of the bone specimens used for E value testing had an effect on the results: Lettry et al. placed the bone in saline at pH 7.4 at all times (or in a -18°C refrigerator for longer periods) and the E value results ranged from 4732- The E values ranged from 4732 to 10077 MPa, whereas the mandibular bone used by Tamatsu et al. was not “fresh” wet bone, but dry mandibular bone measured after wetting, which has been shown to have some alterations in physical properties, and E values ranged from 12600 to 21000 MPa. The inconsistency of the two sets of experimental results was not obtained on the same test bones, so the description of the problem is not sufficient. Cortical bone is dense and hard, and its E value is generally about two orders of magnitude higher than that of cancellous bone at the corresponding site, and the stress value in the former is 20-30 times greater than that in the latter under load. Therefore, the closer the range of cortical bone and cancellous bone in the model is to the actual situation, the closer the calculated results are to the actual measurements. Some scholars have replaced the respective E values of cortical bone and cancellous bone with intermediate E values, and regarded the mandible as a completely homogeneous and isotropic material, but this method is generally used for rough qualitative studies, but it can also reflect some problems easily and intuitively. Most scholars still consider cortical bone and cancellous bone separately. 3.2 Elastic modulus of human mandibular cancellous bone Goldstein et al. found in the study of human proximal tibial cancellous bone that the E values of cancellous bone at different locations in the same metaphysis differed by a factor of 100, indicating that cancellous bone has a high degree of inhomogeneity. These findings confirm Wolff’s law that the different functions of cancellous bone at different anatomical sites directly affect the mechanical properties of its own structure, and therefore, the study of cancellous bone has received increasing attention. Although the main biomechanical characteristics of the mandible are determined by the dense bone, the thickness and number of cancellous bone and bone trabeculae are functionally related, and they are arranged into dental and muscular orbits to transmit masticatory forces. The elastic modulus of mandibular cancellous bone is more complex than that of cortical bone, so some scholars have used cancellous bone parameters from other sites to study mandibular bone. For example, in the study by Hart et al, the E value of mandibular cancellous bone was derived from fibula (whose material parameters of cancellous bone were taken from Dr. Turner’s 1987 paper). Misch et al. demonstrated that the cancellous bone of the mandibular body is homogeneous but non-homogeneous, with E values ranging from 35.6 to 67.5 MPa from the molar to the anterior region, but he concluded that the cancellous bone is slightly “homogeneous” in different regions compared to the mandibular cortical bone. “O “Mahony et al. specifically determined the E value of cancellous bone in a 74-year-old female edentulous patient and concluded that it was isotropic in cross-section. Some authors have assumed that the mechanical characteristics of cancellous bone under certain conditions are not affected by tissue anisotropy (which can be neglected), and this assumption was confirmed by Kabel et al. Mahony et al. obtained the Young’s modulus of the edentulous mandibular cancellous bone in three orthogonal directions by stress tests: the Young’s modulus was greatest in the proximodistal and mesial directions, averaging 907 ± 849 MPa, followed by about 511 ± 565 MPa in the buccolingual direction and 114 ± 78 MPa in the superior and inferior directions. 3.3 Relationship between elastic modulus and strain rate and density of the human mandible McElhaney and Byars performed isokinetic compression tests on human bone with strain rates ranging from 0.001/s to 1500/s, with a corresponding increase in E values from 2.2×106 1b/in2 at low strain rates to 5.9×106 1b/in2 at high strain rates. 106 1b/in2. Brown and Ferguson [20] tested E values for similar strain rate intervals (10-4/s to 10-2/s) and found larger E values at high strain rates, but no statistical difference. carter and Hayes found that E values were correlated with the 0.06th power of the strain rate, and Linde et al. 0.05th power correlation. The results of Bin Bo et al. showed a statistically significant correlation of E values with the 0.052nd power of strain rate. It should also be noted that these reflect the dynamic properties of the mandible, but its strain rate is still not considered high. In China, Yang Guitong et al. made some impact tests of human femur at high strain rates and obtained good experimental information and experience, but there are not many studies for the mandible. As a parameter to describe the structural properties of bone, Martens and Ishida et al. suggested that bone density changes with the mineralization and porosity degree of bone, so it also affects the E value. Rho et al. established linear and nonlinear equations of anisotropic E value and bone density, and the results showed that the E value was positively correlated by bone density, and 1.35-1.75 times the relationship in the nonlinear equation. In China, Bo Bin et al. concluded that E value was correlated with 0.44th power of BMD. Wang Yijin et al. also found that the level of BMD tended to decrease with age and the E value changed accordingly. 4. Factors affecting the elastic modulus of the mandible The elastic constants of the mandible are difficult to obtain from in vivo, and isolated tissue is the main source for obtaining data. However, E values can be affected by a variety of external factors such as the site of extraction, test environment, method, test conditions, specimen fabrication, load direction, and strain rate magnitude, as well as internal factors such as the origin of the specimen species, age, sex, body mass, and the content and arrangement of collagen, the action of living soft tissues, and the feedback regulation of nerves and body fluids. Therefore, the available data on mandibular E values can vary somewhat, and in some cases, significantly. For example, anatomical structures affect the E value of the human mandible: E values vary near the mandibular foramen, at muscle attachments, at the internal and external oblique lines, and at the sublingual glandular fossa, etc. Generally, E values decrease near the concavity, fossa, and foramen and increase in areas where muscle forces are strengthened. Although it is believed that the E value of mandibular cortical bone is almost similar in people aged 60-90 years, most believe that the presence of mandibular teeth affects the E value of mandibular cortical bone: when no teeth are present the mandible is accompanied by some degree of bone resorption, the cortical bone becomes thinner, the mandibular bone body is left at 60% of its original size, collagen fibers change, and conditions such as mineralization change after the loss of teeth, and the bone cancellous located at the base of the The bone cancellous density at the base of the mandible will also increase (compensation after tooth loss), all of which may cause changes in the E value of mandibular cortical bone. The E value of the mandible can be determined by quasi-static mechanical tests or by dynamic tests, the latter of which are more likely to yield higher data. Mandibular E values are generally obtained by standardized and unified mechanical tests of materials, so that the results obtained are credible and easy to compare. Specimens are generally made with reference to ASTM (American Society for Testing and Materials) standards. There are various test methods, for example, some authors found that the length, width and height of the specimen are very critical parameters when solving the E value by the three-point bending test of cortical bone specimens, especially the height h of the specimen, which affects the E value more than other parameters. Lettry pointed out that the length-to-height ratio of the test specimens of Tamatsu and others was about 10, which had a greater influence on the results. Other authors have recently used atomic force microscopy techniques to measure the E values of mandibular cortical and cancellous bone by determining the nanoscale surface deformation curve of the measured tissue with the aid of nanoindentation, which has the advantage of not requiring special specimen preparation techniques; the difference in E values can be determined without affecting the microstructure or composition of the tissue. Since the E values of living mandibles cannot be determined by any destructive experiments, scholars have developed CT techniques and ultrasonic techniques for measuring in vivo E values. There is a linear relationship between the CT value of any point in the bone (Hounsfield) and bone density, and many scholars have established a relationship equation between E value and density, such as the Carter-Hayes empirical formula, so that the E value of a point in the mandible can be derived from the CT value. However, some scholars hold a different view that the structure of the mandible will change due to age, and bone density will become not an accurate predictor of E value, such as Lettry et al. argued that E value has a weak correlation (A weak correlation) with CT value, and using CT value to accurately predict bone material properties is not sufficient. Abendschein and Hyatt found a high correlation between ultrasonic velocity and the E value and density of cortical bone specimens, where the solid can propagate both shear-related transverse waves and capacitance (or length)-related longitudinal waves, and the wave speed of longitudinal waves = (Young’s E value/density)1/2; the wave speed of transverse waves = (shear E value/density)1/2. It should be noted that this equation Yoon and Katz applied the generalized Cosserat theory to study the mechanism of ultrasonic wave propagation in bone, pointing out that the propagation of ultrasonic waves in bone, in addition to viscoelasticity, there may be other mechanisms that are not very clear, such as dispersion.